3(x-2)(5x+3)=0

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Solution for 3(x-2)(5x+3)=0 equation:


Simplifying
3(x + -2)(5x + 3) = 0

Reorder the terms:
3(-2 + x)(5x + 3) = 0

Reorder the terms:
3(-2 + x)(3 + 5x) = 0

Multiply (-2 + x) * (3 + 5x)
3(-2(3 + 5x) + x(3 + 5x)) = 0
3((3 * -2 + 5x * -2) + x(3 + 5x)) = 0
3((-6 + -10x) + x(3 + 5x)) = 0
3(-6 + -10x + (3 * x + 5x * x)) = 0
3(-6 + -10x + (3x + 5x2)) = 0

Combine like terms: -10x + 3x = -7x
3(-6 + -7x + 5x2) = 0
(-6 * 3 + -7x * 3 + 5x2 * 3) = 0
(-18 + -21x + 15x2) = 0

Solving
-18 + -21x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -7x + 5x2) = 0

Factor a trinomial.
3((-3 + -5x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-3 + -5x)' equal to zero and attempt to solve: Simplifying -3 + -5x = 0 Solving -3 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5x = 0 + 3 -5x = 0 + 3 Combine like terms: 0 + 3 = 3 -5x = 3 Divide each side by '-5'. x = -0.6 Simplifying x = -0.6

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-0.6, 2}

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